Mathematics Course Descriptions
MATHEMATICS (MAT)
COURSE DESCRIPTIONS
MAT 1103 Freshman Seminar Credit: 1 hr.
This course is designed to provide entering freshmen and new students with an orientation to the university, its traditions, its program offerings, and its academic requirements and regulations. The focus is on adaptation to college life, problem solving skills, and critical thinking skills including effective study and test taking methods. This course will also provide an orientation to the Department of Mathematics, its various degree paths, and the nature of mathematical reasoning.
MAT 1306 Basic Algebra Credit: 3 hrs.
This course is designed for students with limited proficiency in elementary algebra. Topics include signed number operations, simplifying algebraic expressions, exponents, polynomials, equations and inequalities, word problems, and factoring. Requirements: All students scoring below a given level on the mathematics placement examination must enroll in this course. Students enrolled in this course receive a grade of P or F. Credit for this course is not counted towards the total hours needed for graduation.
MAT 1311 College Algebra Credit: 3 hrs.
This course covers topics in applied algebra. Topics include a review of factoring, algebraic fractions, rational exponents, radicals, first-degree linear equations and graphs, quadratic equations, first-degree inequalities, and linear systems of equations. Prerequisite: MAT 1306 or a satisfactory score on the mathematics placement examination given by the university. This course may not be used as an approved elective by mathematics majors.
MAT 1312 Precalculus I Credit: 3 hrs.
This course introduces techniques for solving inequalities involving absolute value, polynomials, and rational expressions. Included are discussions of functions and their graphs for linear, quadratic, and general polynomials, rational functions, exponentials, and logarithms. General graphing techniques and the conics are also discussed. Prerequisite: MAT 1311 or a satisfactory score on the mathematics placement test.
MAT 1313 Precalculus II Credit: 3 hrs.
This course, a continuation of MAT 1312, helps to prepare a student for Calculus I. The following are among the topics studied: trigonometric functions and identities, solutions of trigonometric equations and triangles, graphs of the trigonometric functions, and verbal problems involving applications of trigonometric functions. Also included are sequences, series and mathematical induction. Prerequisite: MAT 1312 or a satisfactory score on the mathematics placement test.
MAT 1323 Fundamentals of Mathematics Credit: 3 hrs.
This course serves as the core requirement for those students whose departments do not require any more mathematics courses, with the exception of MAT 2326 (Elementary Statistics). Topics include basic algebraic concepts, sets, statistics, probability, mathematics of finance, and problem solving. Prerequisite: MAT 1306 or a satisfactory score on the mathematics placement examination given by the university. This course may not be used as an approved elective for mathematics majors.
MAT 2260 Precalculus Review Seminar Credit: 2-6 hrs.
This course includes a review of topics covered in precalculus courses. The course provides the opportunity for students preparing for licensure and proficiency examinations to review course content and to improve test-taking skills. Credit for this course is not counted towards the total hours needed for graduation. The course may be taken more than once. Prerequisite: MAT 1313 or approval from the instructor. Grade: Pass/Fail.
MAT 2301 Introduction to Computer Algebra Systems Credit: 3 hrs.
This course presents a brief introduction to the software and hardware being used. Included will be work with one or more computer algebra systems, such as Maple, Derive or Mathematica. Time will be spent not only learning to use the software, but using experimentation and discovery to better understand mathematical concepts. Some topics addressed are solutions of equations and inequalities, functions and their graphs, and other pre-calculus and calculus topics. Prerequisite: MAT 2317 or 2333.
MAT 2303 Principles of Mathematics I Credit: 3 hrs
The first of two semesters in a fundamental of mathematics sequence for education majors with the exception of Secondary Mathematics Education and Comprehensive Science. Problem solving, real numbers, numbers theory, decimals, rational numbers, percents, and numeration systems are the mathematics concepts of focus for this course. Prerequisite: Place above MAT 1306 or completion of college math course.
MAT 2304 Principles of Mathematics II Credit: 3 hrs
The second of two semesters in a fundamental of mathematics sequence for education majors except Secondary Mathematics Education and Comprehensive Science. Probability, statistics, algebra, measurement, geometry, and logic are the mathematics concepts of focus for this course. Prerequisite: MAT 2303
MAT 2316 Linear Algebra Credit: 3 hrs.
This course presents systems of linear equations and matrices, determinants, vector spaces, linear transformations and their matrix representations, Eigen values, eigenvectors, and some applications. Prerequisite: MAT 2317.
MAT 2317 Calculus I Credit: 3 hrs
This course is the first of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. The course examines functions, graphs, limits and derivatives, and rules of differentiation. This includes differentiation of polynomial, rational, trigonometric, logarithmic, exponential functions, application of differentiation and the use of computational tools. Prerequisite: MAT 1313 or advanced placement. This course will not count with MAT 2333.
MAT 2318 Calculus II Credit: 3hrs
This course is the second of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. The course examines techniques and applications of integral calculus, improper integrals, elementary differential equations, and the use of computational tools. Prerequisite: MAT 2317.
MAT 2321 Foundations of Modern Mathematics Credit: 3hrs
This course is designed for mathematics and mathematics education majors as an introduction to mathematical principles and reasoning. It gives an introduction to the discipline of mathematics emphasizing deductive arguments and the development of analytical skills needed in understanding and building mathematical arguments. The content will include an introduction to logic and methods of proof and takes a look at functions and the " #! definition of continuity. The course also examines the algebraic and topological properties of R and introduces metric spaces. Prerequisite: MAT 2317.
MAT 2326 Elementary Statistics Credit: 3 hrs.
The major emphasis of this course is on the use of statistics as a tool in the decision-making process. The following are among the topics to be developed: common statistical measures, graphing techniques, probability, the binomial distribution, the standard normal distribution, t-tests, correlations and prediction, chi-square, and analysis of variance. (Cross-listed with SOC 2326 and PSY 2326).
MAT 2333 Calculus for Business Majors Credit: 3 hrs.
This course includes a brief review of the concepts of functions and combinations of functions. It also covers the basic concepts of differential and integral calculus and its applications. Special attention is given to problems in business and economics. Prerequisite: MAT 1312 or approval from instructor.
MAT 2337 Discrete Mathematics Credit: 3 hrs.
Topics include mathematical logic, Boolean algebra and computer logic, proof techniques, set theory, combinatorics, finite state machines, and complexity of algorithms. Prerequisite: MAT 1313.
MAT 3260 Mathematics Review Seminar Credit: 2-6 hrs.
This course includes a review of topics covered in core mathematics courses for majors. The course provides the opportunity for students preparing for licensure and proficiency examinations to review course content and to improve test-taking skills. Credit for this course is not counted towards the total hours needed for graduation. The course may be taken more than once. Prerequisites: MAT 2316, MAT 3412, MAT 3341, or approval from the instructor. Grade: Pass/Fail.
MAT 3310 Probability and Statistics I Credit: 3 hrs.
This course is designed to give an introduction to set theory and probability theory and to the concept of random variables, both discrete and continuous. Consideration is given to a discussion of several standard types of distributions. Prerequisites: MAT 2318.
MAT 3311 Probability and Statistics II Credit: 3 hrs.
This course is a continuation of MAT 3310. Treatment is given to random sampling and classical statistical inference, especially point and interval estimation, tests of hypotheses, general linear models, Bayesian methods, and an introduction to least squares. Prerequisite: MAT 3310, MAT 3317.
MAT 3312 Biostatistics Credit: 3 hrs
This course covers topics in both probability and statistics including: probability function and its properties, discrete and continuous random variables and their probability distributions, data description and their presentation, hypothesis testing, decision making and experimental design. Data will be used from the areas of biology, psychology and neuroscience with appropriate software. Use of computer is a requirement. This course is for sophomore/junior level students with major or minor in an area of life science. Prerequisite: MAT 1312 and Bio 1315 (Introduction to Biotechnology).
MAT 3316 Calculus III Credit: 3 hrs
This course is the third of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. Course includes sequences, infinite series, power series, Taylor's Theorem, conics and parametric equations, polar coordinate system, vectors and geometry of space, vector-valued functions and the use of computational tools. Prerequisite: MAT 2318.
MAT 3317 Calculus IV Credit: 3 hrs
This course is the fourth of four sequential semester courses which addresses calculus for mathematics, science and engineering majors. Course examines the functions of several variables, partial derivatives, gradients, directional derivatives, maxima and minima, multiple integration, line and surface integrals, Green's Theorem, Divergence Theorems, Stokes' Theorem, applications and the use of computational tools.
Prerequisite: MAT 3316.
MAT 3320 Introduction to Number Theory Credit: 3 hrs.
Topics covered in this course include divisibility properties of the integers, primes, congruencies, Diophantine equations, and primitive roots. Prerequisite: MAT 2317.
MAT 3326 Geometry Credit: 3 hrs.
This course presents Euclidean and non-Euclidean geometry from a modern perspective. Topics include congruence, parallelism, similarity, measurements, constructions, solid geometry, ratio, proportion, the parallel postulate, and an overview of non-Euclidean geometries. Direct and indirect proofs will also be studied. Prerequisite: MAT 2337.
MAT 3340 Introduction to Numerical Analysis Credit: 3 hrs.
This course covers theory and application of algorithms for numerical computation, approximation, interpolation, numerical differentiation and integration, solution of linear and ordinary differential equations. Prerequisites: CSC 1311 and MAT 2316. (Cross-listed with CSC 3340)
MAT 3341 Algebraic Structures I Credit: 3 hrs.
This course introduces the basic algebraic properties of groups, rings, and fields. Prerequisites: MAT 2316 and MAT 2337. (Cross-listed with CSC 3341)
MAT 3342 Algebraic Structures II Credit 3 hrs.
This course is a continuation of MAT 3342, Algebraic Structures I. Topics include normal subgroups, quotient groups, direct sums, Abelian groups, rings, integral domains, fields, ideals and maximal ideals,quotient rings, homomorphisms, polynomial extensions of rings, divisibility on commutative rings, and factorization of polynomials. Prerequisite: MAT 3341.
MAT 3350 Linear Programming Credit: 3 hrs.
This course develops the techniques used in linear programming such as the simplex method and the duality method. Linear programming techniques will be applied in the solution of transportation problems, industrial problems and problems in economic theory. Prerequisites: MAT 2316 and CSC 1311.
MAT 3356 Independent Study Credit: 1-6 hrs.
This course provides an opportunity for mathematics majors at the junior and senior level to work on an independent project with the guidance of a faculty member. The project may consist of a combination of review of research, a research project, or a research paper. Topics covered in this course are not offered in formal courses. This course may be repeated if a student has not earned the maximum of six semester hours. This course is limited to junior and senior mathematics majors and subject to the approval of the instructor and chair.
MAT 3391 Mathematics Co-Op Credit: 3 hrs.
(See the course description for the Cooperative Education course number 3391 in the Undergraduate Catalog.)
MAT 3691 Mathematics Co-Op Credit: 6 hrs.
(See the course description for the Cooperative Education course number 3691 in the Undergraduate Catalog.)
MAT 4301 Differential Equations I Credit: 3 hrs.
This course develops techniques for solving differential equations, presents theory to support those techniques, and includes applications of differential equations. The course includes the study of equations of order one, linear differential equations, non-homogeneous equations, the Laplace transform, and systems of equations. Prerequisite: MAT 2318.
MAT 4302 Differential Equations II Credit: 3 hrs.
This course covers some methods for finding solutions of differential equations not considered in MAT 4301. It includes non-linear differential equations, power series solutions of differential equations, Fourier series, and an introduction to methods of solutions of partial differential equations of mathematical physics: heat and wave equations. Prerequisite: MAT 4301 and MAT 3317.
MAT 4304 History of Mathematics Credit: 3 hrs.
This course is a chronological study of the development of mathematics. It includes those mathematicians and periods in which the study of certain areas of mathematics prevailed. Prerequisite: MAT 2317.
MAT 4311 Real Variables I Credit: 3 hrs.
This course presents the real numbers, least upper bound and greatest lower bound, sequences and series of real numbers, monotone and Cauchy sequences, limit superior and limit inferior, metric spaces, connected, complete and compact metric spaces, continuous functions on metric spaces, sequences and series of functions, and the three famous theoremsâ??Weierstrass Approximation Theorem, Picard Existence Theorem, and the Ascoli-Arzela Theorem. Prerequisite: MAT 3317.
MAT 4312 Topology Credit: 3 hrs.
This course will cover operations on sets, properties of functions, topology of the real line, metric spaces, topological spaces, connectedness, compactness, and product and quotient spaces. Prerequisite: MAT 3317 or permission of instructor.
MAT 4313 Real Variables II Credit 3 hrs.
This course is a continuation of MAT 4311, Real Variables I. This course extends the study to include the topology of Euclidean spaces, differentiability in Euclidean Spaces, and metric spaces. Sequences of functions, uniform convergence, convergence of series, and power series will also be covered. Prerequisite: MAT 4311.
MAT 4315 Advanced Calculus Credit: 3 hrs.
This course presents differential and integral calculus of functions with domain and range in Euclidean nspace. Topics include geometry of n-space, sequences and series in n-space and of functions, uniform convergence, improper integrals with parameters, Fourier series, extrema, differentiation of transformations, implicit function theorems, transformations of multiple integrals, differential forms, and Green, Gauss, and Stokes Theorems in a general set up. Prerequisite: MAT 3317.
MAT 4330 Directed Study Seminar Credit: 3 hrs.
Students may enroll for study of an area of mathematics not given in a formal course. Approval must be given by the department chair and the instructor. All parties must agree on the course format and content. This course is limited to senior mathematics majors.
MAT 4331 Mathematical Modeling Credit: 3 hrs.
Mathematical model building in both discrete and continuous cases will be developed. A variety of mathematical problems in physical, biological, social, and behavioral sciences will be discussed. Specific problems will be given in applied dynamical systems, differential and integral equations and some statistical processes. In every topic, the emphasis will be on construction, interpretation, analysis, simulation, and testing of models. Prerequisites: MAT 3317, MAT 4301, MAT 3310, and CSC 1311.
MAT 4332 Introduction to Statistical Methods Credit 3 hrs.
This course covers data analysis, sampling, probability, standard methods of statistical inference, including ttests, chi-square tests, and nonparametric methods. Applications include the use of a statistical computer package. Prerequisite: MAT 2317.
MAT 4333 Methods of Regression/Analysis of Variance Credit 3 hrs.
This course includes simple and multiple regression, model selection procedures, analysis of variance, simultaneous inference, and the design and analysis of experiments. Applications include the use of a statistical computer package. Prerequisite: MAT 4332.
MAT 4352 Principles of Teaching Mathematics Credit: 3 hrs.
This course is designed for students preparing to teach secondary school mathematics. Innovative techniques to be used in the teaching of mathematics and assessment procedures will be discussed and developed. No credit is allowed for work of less than C quality. (The course is three periods per week.) Prerequisite: Admission to teacher education program. (Cross-listed with EDU 4352)
MAT 4355 Operations Research Credit: 3 hrs.
This course develops some standard operations research techniques including model formulation, PERT problems, transportation problems, linear programming, dynamic programming, Markov analysis, and queuing models. Prerequisites: MAT 3311 and CSC 1311.
MAT 4356 Mathematical Statistics I Credit 3 hrs.
This course includes probability, random variables and their distributions, mathematical expectation, moment generating functions, and sampling distributions. Prerequisite: MAT 3317.
MAT 4357 Mathematical Statistics II Credit 3 hrs.
This course is a continuation of MAT 4356; Mathematical Statistics I. Topics include estimation and hypothesis testing, applications of statistical inference, introduction to regression, and correlation. Prerequisite: 4356.
MAT 4386 Automata, Formal Languages and Computability Credit: 3 hrs.
This course studies computer science theory and the mathematical foundations of digital computers. Its topics include the family of computing machines (finite-state, push-down and Turing), the Chomsky hierarchy of languages, decidability, unsolvable problems, and applications of automata to areas of syntactic analysis, modeling, and artificial intelligence. Prerequisites: CSC 4340 and MAT 2316, or consent of instructor. (Cross-listed with CSC 4386)
MAT 4387 Senior Seminar I Credit 3 hrs.
This course contains lectures, dialogues, and readings in mathematical topics in order to reinforce the knowledge and skills learned in core courses thus far. This course provides the opportunity for students to look at applications and problems in order to prepare for proficiency and licensure exams such as the GRE or first actu exam. The students will be asked to read journal articles and give summary presentations in class. Prerequisite: MAT 4311.
MAT 4388 Senior Seminar II Credit 3 hrs
This course includes readings and weekly student lectures or student-led discussions on a variety of mathematical topics determined by the interest of the students and the instructor. Emphasis will be placed on independent research and clear exposition. A paper is required. Prerequisite: MAT 4387.
MAT 4391 Mathematics Co-Op Credit: 3 hrs.
(See the course description for the Cooperative Education course number 4391 in the Undergraduate Catalog.)
MAT 4691 Mathematics Co-Op Credit: 6 hrs.
(See the course description for the Cooperative Education course 4691 in the Undergraduate Catalog.)
MAT 4981 Observation, Student Teaching and Practicum Credit: 9 hrs.
This course deals with the application of theory to teaching situations in the secondary schools. During the first six weeks, students spend one-half day in a classroom setting, engaging in directed observation, small group tutoring and part-time classroom teaching. The final ten-week period is devoted to full-time student teaching in the same classroom setting. Proficiency in training and handling typical classroom situations is developed. This course is required for secondary education majors. Prerequisite: Approval by the Teacher Education Committee and the major department. (Cross-listed with EDU 4981)
